We study the low-temperature properties of a classical Heisenberg model with site-random interlayer couplings on the cubic lattice. This model is introduced as a simplified effective model of Sr(Fe$_{1-x}$Mn$_{x}$)O$_2$, which was recently synthesized. In this material, when $x=0.3$, $(πππ)$ and $(ππ0)$ mixed ordering is observed by neutron diffraction measurements. By Monte Carlo simulations, we find an exotic bulk spin structure that explains the experimentally obtained results. We name this spin structure the "random fan-out state". The mean-field calculations provide an intuitive understanding of this phase being induced by the site-random interlayer couplings. Since Rietveld analysis assuming the random fan-out state agrees well with the neutron diffraction pattern of Sr(Fe$_{0.7}$Mn$_{0.3}$)O$_2$, we conclude that the random fan-out state is reasonable for the spin-ordering pattern of Sr(Fe$_{0.7}$Mn$_{0.3}$)O$_2$ at the low-temperature phase. ; Comment: 13 pages, 12 figures